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In Pseudo code:
var MyArray = new Array(1, 2, 3, 4, 5);
var MyIndex = Random.Range(0,(MyArray.length - 1));
Debug.Log(MyArray[MyIndex]);
For every loop, remove the MyArray[MyIndex] from the array, and you will never reuse the already used position.
You migt consider using a List instead, since you have Add, Remove methods, where Arrays require some more housekeeping.